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 A191471 E.g.f. (1+arctan(x))^arctan(x) 0

%I

%S 1,0,2,-3,4,-30,162,-252,400,-27912,200744,705672,-4202296,-223340208,

%T 1418238416,29398266888,-114981277184,-8193860510784,30889433635776,

%U 2261786651427072,-3830504174333824

%N E.g.f. (1+arctan(x))^arctan(x)

%F a(n)=sum(m=1..n, sum(j=0..(n-m)/2, (2^(2*j-n)*(n-2*j)!*stirling1(n-m-2*j,m)*(-1)^j*sum(i=0..2*j, (2^(i+n-2*j)*stirling1(i+n-2*j,n-2*j)*binomial(n-1,i+n-2*j-1))/(i+n-2*j)!))/(n-m-2*j)!));

%t With[{nn=30},CoefficientList[Series[(1+ArcTan[x])^ArcTan[x],{x,0,nn}], x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 01 2011 *)

%o (Maxima)

%o a(n):=sum(sum((2^(2*j-n)*(n-2*j)!*stirling1(n-m-2*j,m)*(-1)^j*sum((2^(i+n-2*j)*stirling1(i+n-2*j,n-2*j)*binomial(n-1,i+n-2*j-1))/(i+n-2*j)!,i,0,2*j))/(n-m-2*j)!,j,0,(n-m)/2),m,1,n);

%K sign

%O 0,3

%A _Vladimir Kruchinin_, Jun 03 2011

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Last modified January 24 00:05 EST 2022. Contains 350515 sequences. (Running on oeis4.)